I think that UE only detect new tracking area and sends tracking area update to MME. I never heard or read that MME triggers TAU procedure for an UE.
There are two types of trigger for TAU.
1. Periodic TAU:
In case of periodic TAU, UE sends TAU request to MME irrespective of any change in current tracking area.
2. A-periodic TAU:
whenever an UE detects a new tracking, it reports to MME when UE is in RRC idle mode.